If it looks like a duck…

Last week I attended, and spoke at, a session entitled “Frontiers of Scanning Probe Microscopy” at this year’s Microscience Microscopy Congress in Manchester. The focus of the presentation I gave there — and it’s a recurrent theme in the talks and seminars I give at the moment — was the thorny problem of identifying and interpreting artefacts in images of atoms and molecules.

Microscopists tend to be skeptical about that old maxim, “seeing is believing”. But, as I’ll show below, sometimes we’re simply not skeptical enough. This is not just an issue for those involved in imaging and microscopy — it’s at the core of all science: how do we know our measurements are an accurate picture of reality? (Whichever version of reality we prefer…).

Every image out there, regardless of how it was created, is a convolution of the properties of the object and the characteristics of the imaging system. (And that includes our eyes). The word convolution has its roots in the Latin convolvere, meaning “to roll together”. That’s a great description of the mathematical physics underpinning the process: the functions describing the object and the imaging system are indeed rolled together (via a convolution integral).

Twenty-five years ago, the Hubble telescope gave us a spectacularly (un)illuminating insight into the essence of convolution. The images below, taken from the Wiki page for the HST, vividly show the effects of the convolution process when the imaging characteristics of the telescope were, let’s say, rather poor (on the left) and when they were much improved by the addition of corrective optics (on the right).

Hubble_Images_of_M100_Before_and_After_Mirror_Repair_-_GPN-2002-000064

The imaging system — and this holds true for any imaging system, be it a microscope, telescope, camera, or whatever arbitrary combination of optics we put together — is characterised via a very simple concept: the point spread function. That function does exactly what it says on the tin: it captures how the image of a single point in the object spreads in space as a result of the imaging system. We then take the point spread function and apply it in turn to all of the points in an object in order to determine what the resulting image will be. For the HST images above, the point spread function is substantially broader for the image on the left than for that on the right.

I should stress that these types of convolution effect are, of course, not limited to images — they hold for any measurement and any type of signal. Ten years ago, I taught an undergraduate module on Fourier analysis and spent quite some time on convolution. (I’ll save the elegance of the Fourier treatment of convolution for a future post). I used the various sound samples below to show the students how convolution works for an audio, rather than a visual, signal. In this case, the point spread function is the response of the surroundings (be it a cave, lecture theatre, auditorium, forest, classroom…) to a very short, sharp signal: the audio equivalent of a single pixel or point. Think of it like making one short hand-clap in a room: the point spread function, which for audio signals is called the impulse response function, is the sound of that clap reverberating. (Yes, the hand-clap is just an approximation to the type of short, sharp signal — i.e. impulse — we need but it serves to make the point.)

So, let’s take a large concert hall. Here’s the impulse response for the hall:

Now consider a space which is rather less grand (at least in terms of its audio characteristics). An ice cavern, say…

Note the very audible differences between the impulse response for the concert hall and for the cavern.

Now let’s take an audio signal completely at random. Like this…

If we convolve the Pythons’ Gregorian chant with the impulse response for the concert hall, here’s what we get.

And this is the convolution of the chant with the impulse response for the ice cavern:

Just as with the HST images, the response of the system (the concert hall or the ice cavern in this case) can be worked out from its audio “point spread function” (the impulse response).

For scanning probe microscopy (SPM), however, we’re in a whole new world of pain when it comes to deciphering the contribution of the imaging system to the image we see. Far from being a static distortion as in the HST optics, the scanning probe itself responds dynamically to the object under study. The simple point spread function approach breaks down. And this can lead to some very misleading images indeed…

My first love in research was, and will always be, SPM. I’ve written about the power and pitfalls of the technique in detail before but the concept at the heart of the technique is really very simple indeed. (Its execution rather less so). We take an exceptionally sharp probe — terminated in a single atom or molecule — and move it very close to a surface, an interface, or a single atom or molecule. When i say “very close”, I mean within a few atomic diameters, or, in the highest resolution work, about a single atom’s distance from a surface. At those distances a number of forces and interactions come into play including, in particular, chemical bond formation and, as described in this post for the Institute of Physics’ physicsfocus blog last year, electron-electron repulsion due to the Pauli exclusion principle. By scanning the probe back and forth (using piezoelectric motors) we can measure the variation of those forces within a single molecule and convert that signal to an image.

Leo Gross and co-workers at the IBM research labs at Rüschlikon in Zurich pioneered a new sub-field of scanning probe microscopy when they showed back in 2009 that images of the internal architecture of single molecules could be captured. The agreement between these images and the ball-and-stick models used by chemists (and physicists) to represent molecules is striking, to put it mildly. While the picture of the tip in the figure to the right is an artist’s representation, the image of the molecule directly below is the actual experimental data measured for a single pentacene molecule, the ball-and-stick model for which is shown at the foot of the figure (grey spheres are carbon, white spheres are hydrogen — it’s a molecule so simple even physicists can understand it.)

PWNANOMay16-AFM1.jpg

Ultrahigh resolution images showing submolecular structure in exquisite detail for a variety of molecules followed (as described in this book chapter). But a number of SPM research groups across the world, including our team at Nottingham, were particularly keen to ascertain whether intermolecular bonds (rather than, or in addition to, intramolecular bonds) could be resolved using the method introduced by IBM Zurich. Nottingham has a long track record — through the efforts of the research groups of my colleagues Peter Beton and Neil Champness — of exploiting hydrogen bonds in the assembly of supramolecular systems. Hydrogen bonds are also of key importance in biochemistry, including, of course, in underpinning base pair interactions in DNA. Could we actually see hydrogen bonds between molecules using probe microscopy?

We started the experiments.

And we were over the moon when we acquired this image of a hydrogen-bonded lattice of molecules shortly afterwards…

NTCDI

 …particularly as we could apparently map the “filamentary” features between the molecules directly onto where we expected the hydrogen bonds (the dotted lines in the image below) to be:

NTCDI-H-bonds.png

While we were puzzling over how to interpret the image — just why did the hydrogen bonds appear so bright compared to the bonds inside the molecules? — we were somewhat less over the moon to be scooped on the first ‘observation’ of hydrogen bonds, as described in the article below. (Click on the image for the full Chemistry World piece).

85828_hydrogen-visualisation_zhang_630m

Note the social media hits on that article: the images certainly created a stir.

Once more it looks like there’s exceptionally good agreement between the positions of the hydrogen-bond features in the probe microscope image on the left above and those expected on the basis of the chemistry (as sketched in the diagram to the right).

But, again, why are the H-bonds so bright in the image? The authors’ own calculations showed that the electron density between the molecules could not account for the brightness — there just wasn’t enough charge there. (This chimed with our experience, as we described in a paper published a few months later. (Free to read — no paywall)).

Even though the positions of the features in the images met all of our expectations with regard to where we’d expect hydrogen bonds to be observed, was it possible that it was simply some type of image artefact? Were those ‘bonds’ nothing more than nanoscopic will-o’-the-wisps? Could Nature really be that cruel? (That’s Nature as in the universe around us, not Nature the journal. Scientists all know just how cruel Nature can be…).

Yes, Nature is that cruel.

It turns out that the intermolecular features readily appear in simulations based around the type of simple interatomic potentials we explain to our 1st year undergraduate students. (See, for example, the sections on Lennard-Jones and Morse potentials in Chapter 2 of this ebook). The simulations in question know nothing about the electron density due to bonding between the molecules — they are based solely on the atomic coordinates, i.e. the positions of the atoms in the molecules. And yet, as the images below show, the simulations — which have been developed by a number of groups in parallel, particularly those of Pavel Jelinek at the Academy of Sciences of the Czech Republic and Peter Liljeroth at Aalto University in Finland — provide exceptionally good agreement with the experimental images. (The figure below is taken from this paper by Prokop Hapala and co-workers in Jelinek’s group, along with a team at Forschungszentrum Juelich comprising Stefan Tautz, Ruslan Termirov, Christian Wagner and Georgy Kichin).

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So if we’re not really seeing bonds, just what is going on?

When acquiring ultrahigh resolution images of the type pioneered by Leo Gross and colleagues, it is generally the case that the tip is terminated — either deliberately or inadvertently — with a single molecule. (The eagle-eyed among you might have noticed the CO molecule hanging off the end of the tip in the artist’s impression of the pentacene imaging experiment above). The molecular probe can flex and pivot as it is dragged across the target molecule — the apex of the tip bends back and forth due to the forces it experiences from the atoms of the molecules underneath. And that bending motion gives rise to the intermolecular features.

No intermolecular bonds required.

In a clever experimental design, Sampsa Hämäläinen, Liljeroth and co-workers used a molecule which forms hydrogen bonds at some places, but not at others, to highlight the exceptionally important role of the probe in generating spurious intermolecular features. The same type of effect has also been observed for halogen bonding and, most recently, for a system where no intermolecular bonds at all are expected: a lattice of buckyballs (C60 molecules). (I presented these latter data at the conference in Manchester.)

What’s more, and to add to the pain, even if we ‘lock down’ the probe molecule in the simulations — which we did for our calculations — so that it can’t flap around, we’re still left with the point spread function to contend with. The probe has a finite width (in terms of its electron ‘cloud’) and, as pointed out by Hapala and colleagues, this can also generate artefacts via convolution between the probe and the target molecule.

Douglas Adams once said

If it looks like a duck, and quacks like a duck, we have at least to consider the possibility that we have a small aquatic bird of the family anatidae on our hands.

It’s indeed possible. But when it comes to science, it can look like a duck, waddle like a duck, and quack like a duck…

…but all too often it can be a goose.